I am not sure of using no and not in case an adjective follows. What is the right one between two examples below?
Period of access providing (not longer than 1 year)
Period of access providing (no longer than 1 year)
The usage of no/not with nouns is clear, but with adjective it is confusing.
If I rephrase your sentence to something like we provide a period of access (no / not) longer than 1 year, then both versions are grammatical.
To me, no longer sounds more natural, while not longer seems more formal. However, that's mostly a personal opinion.
In terms of idiomatic use, Google Books NGram Viewer suggests that no longer is the more common of the two (at least in writing):
